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Opial and Pólya type inequalities via convexity

Saker S. H., Abdou D. M., Kubiaczyk I.

Fasciculi Mathematici

2018

Nr 60

145--159

In this paper, we prove some new dynamic inequalities related to Opial and Pólya type inequalities on a time scale T. We will derive the integral and discrete inequalities of Polya’s type as special cases and also derive several classical integral inequalities of Opial’s type that has been obtained in the literature as special cases. The main results will be proved by using the chain rule, Hölder’s inequality and Jensen’s inequality, Taylor formula on time scales.